I'm really sad to hear that David Levine has died; his professional presence was immense. He was always a fine cartoonist – and an especially fine caricaturist – who defined a style copied by a lot of people. I don't think there's any hard-and-fast rules to describe exactly what he did, but Levine stood out because he was so very good at it; he had great scope.

I met him once at a colloquium about humour at Cambridge University. I never got to know him well, but he was there with Jules Feiffer, another one of the greats. They were both witty, very funny, and had that whole Jewish New York thing going on: dry, distinguished and elderly. As a progressive leftie with a speciality for caricature, he was, I think in an American context, becoming more and more an anomaly.

I know he had another life as a painter. I don't know if he regarded this as his true art, but his caricatures [for the New York Review of Books] were more than enough; they were an art in themselves. Levine gave the big-head, tiny-body idea, with the head emphasised and the body almost an afterthought, a very distinctive, modern stamp. A lot of people who draw in that style owe a lot to him, and while he didn't invent it, he was and will remain a big influence. I've never done the big set-piece caricatures Levine was about – I've always stuck to strip cartoons – but of course I'll miss his work.

I think the one drawing for which people will remember him most was his Lyndon B Johnson piece from 1966. He drew the president staring straight ahead, with his shirt open, pointing to an operation scar on his body. The scar being a map of Vietnam. Levine was sharp. He aimed at enough politicians with enough props in his lifetime to be recognised as one of the greatest satirists of our age. He was never flabby in his drawing or his subjects; he had a very penetrating line. Of his own job, I think he put it best himself when he said: "Anytime I can bring a god down to human scale, so people can say, 'Gee, Johnson has big ears just like my kid', I'm delighted."